Stochastic Analysis of Scaling Time Series

Multi-scale systems, involving complex interacting processes that occur over a range of temporal and spatial scales, are present in a broad range of disciplines. Several methodologies exist to retrieve this multi-scale information from a given time series; however, each method has its own limitations. This book presents the mathematical theory behind the stochastic analysis of scaling time series, including a general historical introduction to the problem of intermittency in turbulence, as well as how to implement this analysis for a range of different applications. Covering a variety of statistical methods, such as Fourier analysis and wavelet transforms, it provides readers with a thorough understanding of the techniques and when to apply them. New techniques to analyse stochastic processes, including empirical mode decomposition, are also explored. Case studies, in turbulence and ocean sciences, are used to demonstrate how these statistical methods can be applied in practice, for students and researchers.

• This book is the culmination of the authors' research over recent years, in which they have developed several new methods to deal with nonlinear and scaling time series
• Applicable to many different fields of the natural sciences
• MATLAB codes and experimental data are provided online, allowing the reader to reproduce the examples in the book and apply these methods to their own data